# if f(x)=-2x-1 and g(x) =x^2-4 what is fog(-2) We need to determine the composite function.

`(f o g)(x) = f(g(x))`

`=f(x^2-4)`

It means that we need to substitute `x^2-4` in the value of x in f(x). So we have

`(f o g)(x)= -2(x^2-4)-1`

`=...

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We need to determine the composite function.

`(f o g)(x) = f(g(x))`

`=f(x^2-4)`

It means that we need to substitute `x^2-4` in the value of x in f(x). So we have

`(f o g)(x)= -2(x^2-4)-1`

`= -2x^2+8-1`

`=-2x^2+7`

Therefore,

`(f o g)(-2) = -2(-2)^2+7`

` =-2(4)+7`

` =-8+7`

`=-1`

Approved by eNotes Editorial Team If `f(x) = -2x -1`   and `g(x) = x^2 - 4`  , find `fog(-2).`

First,`fog(-2)` is equivalent to `f(g(-2)).`

Next, find `g(-2).`

`g(-2) = (-2)^2 - 4`

`g(-2) = 4 - 4`

Therefore, `g(-2) = 0.`

Now substitute 0 for g(-2) into f(g(-2)).

`f(g(-2)) = -2(0) - 1`

`f(g(-2)) = 0 -1`

Therefore, the solution for fog(-2) = -1.

Approved by eNotes Editorial Team To compose a function f with a function g means to replace the argument x of f with the entire function g. Thus

fog(x) = f(g(x)) = -2*(x^2-4) -1 =-2x^2+8 -1 =-2x^2 +7

Therefore

(fog)(-2) =-2*(-2)^2 +7 =-2*4 +7 =-8+7 =-1